A gas in a cylinder with a movable piston is compressed. During the compression, the gas releases 180 J of heat to the surroundings, and the internal energy of the gas increases by 420 J. How much work is done on the gas by the piston?
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Correct answer
B. 600 J
Principle or equation
The first law of thermodynamics: ΔU = Q + W, where Q is heat added to the system (positive if added, negative if released) and W is work done on the system (positive if work is done on the gas).
Why this answer is correct
The gas releases heat, so Q = -180 J. The internal energy increases, so ΔU = +420 J. Using ΔU = Q + W, we have 420 = -180 + W, so W = 600 J. This is the work done on the gas by the piston.
Example
If a gas absorbs 100 J of heat and does 40 J of work on the surroundings, then Q = +100 J and W = -40 J (since work done by the gas is negative work done on the gas). ΔU = 100 - 40 = 60 J.
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